Republicans have made the president’s health care law their primary ammunition in congressional campaigns since 2010 — but embattled Senate Democrats believe they have found an opening to turn voter ire toward the GOP this cycle: Medicaid expansion.

In 20 states, Republican governors have so far rejected a key piece of the health care law — federal aid to expand Medicaid for some of their states’ poorest citizens. Three of those 20 states — Alaska, Louisiana and North Carolina — are home to some of this cycle’s most competitive Senate races, where three incumbents up in 2014 voted for the law.

In the states that accepted federal aid to expand the health care program, the expansion has proved to be one of the rare early successes in the glitch-riddled launch of the landmark overhaul. That has given vulnerable Democratic senators in Alaska, Louisiana and North Carolina an opening to run against their home-state GOP governors in 2014.

“Yes. I have talked about it,” Sen. Mary L. Landrieu, D-La., said Tuesday between votes. “I have been trying to lead a broad coalition of Democrats and Republicans, rich and poor, business interests and consumers alike, to explain to Governor [Bobby] Jindal that the decision he made was not right. It is not in Louisiana’s economic interest, leaving $16 billion on the table.

“Every newspaper in my state — virtually every newspaper in my state — has editorialized for the expansion of health care so middle-class, working people can get coverage,” Landrieu continued. “And you, know, the governor travels all over the world bringing companies that will spend hundreds of millions of dollar to our state, well, this is $16 billion he’s just said ‘no’ to.”

Republican governors in Alaska, Louisiana and North Carolina opted out of $1.4 billion, $15.7 billion and $39.6 billion in aid, respectively, according to a Kaiser Family Foundation report. Estimates suggest that 40,000 Alaskans, 240,000 Louisianans and 500,000 North Carolinians are not getting Medicaid coverage offered under the plan that GOP governors in those states rejected.

The federal government would have paid 100 percent for the first three years of the program, after which states would pay no more than 10 percent of the costs for the expansion. Governors who rejected federal aid have said the ultimate cost of expansion to the state still would be too high, and they received significant conservative accolades for saying so.

“In our state, everyone from the Chamber of Commerce on down supports Medicaid expansion,” said Sen. Mark Begich, D-Alaska, who is seeking re-election. “It’s about 40,000 Alaskans who will not get care because of the governor and honestly, my opponents support the governor’s position. They might be the ... only ones who don’t support giving Medicaid.”

Begich conceded that the Medicaid argument is necessary, but not sufficient for Democrats in 2014 defending their health care votes.

“I think it’s a piece, it’s not by itself, a total, single driver,” Begich said. “And when people see the politics of the people who are running against me — who want to make sure 40,000 Alaskan families don’t have health care when it’s available right now by just making one decision, I think it will have an impact to some voters, no question about it.”

Republican operatives say the other “pieces” of the health care story will be enough to defeat Democrats and win the Senate majority. They insist that Democratic attempts to focus on Medicaid will prove futile if President Barack Obama’s approval ratings remain low and opposition to the health care law as a whole remains high. Multiple aides approached for this story suggested that separating out examples like rejected Medicaid expansion or state failures to establish their own exchanges would be “too nuanced” for an electorate that seems broadly disenchanted by the law.

“Politicians who seem to understand very little about the health care system running back and using this as a talking point shows how truly out of touch they are,” said National Republican Senatorial Committee spokesman Brad Dayspring, who noted the 2014 elections would be well in the rearview mirror for Democrats campaigning on Medicaid expansion by the time state bills come due in 2016. “It’s a lot of federal dollars [to turn down], but you know, rob Peter, pay Paul. Who’s paying those dollars? The taxpayers are.”

Meanwhile, national Democratic operatives said their candidates would launch wholesale defenses of the health care law on the trail. Democrats on the ground in some of these key states believe that going on the offensive against Republican opponents and challenging the decisions made in-state will help create separation between these incumbents and their conservative challengers.

This fight will be especially interesting in North Carolina, where the speaker of the state House, Thom Tillis, is a GOP front-runner to challenge Democratic Sen. Kay Hagan. Tillis backed Republican Gov. Pat McCrory’s decision to reject federal aid through the Medicaid expansion.

In December, Senate Majority PAC, a super PAC that boosts Senate Democrats, spent more than $700,000 on ads supporting Hagan and attacking Tillis for “siding with insurance companies.”

One North Carolina Democratic aide said that zeroing in on the Medicaid expansion issue will “definitely” be central to the case Hagan will try to make to voters in her tight race for re-election.

“If you look at any of our fact-checking and response, that’s key to our message,” the aide said.

Last week, Hagan made a relatively rare national television appearance on MSNBC and turned almost any question she received on the health care law back to expansion.

“It’s absolutely something that will be discussed because this is a very clear contrast. [North Carolina] is really the perfect test case for this, because of what the legislature did ... with their newfound conservative power,” the aide continued, pointing to cuts in teacher pay, tax breaks implemented for the wealthy, cuts to unemployment benefits and the elimination of the state’s earned income tax credit.